His contract expires at the end of this month and the Welsh FA are eager for him to stay on.
Coleman is the country's most successful ever manager, having guided the Dragons to the semi-finals of Euro 2016.
But he could now walk away from the post he has held since 2012, with speculation mounting that he is line to take charge of Sunderland.
Bookmakers have slashed odds on Coleman becoming Black Cats boss, with reports suggesting he is ready to take on the challenge of transforming the Championship strugglers.